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We present an approach to automate the process of discovering optimization methods, with a focus on deep learning architectures. We train a Recurrent Neural Network controller to generate a string in a domain specific language that…

Artificial Intelligence · Computer Science 2017-09-25 Irwan Bello , Barret Zoph , Vijay Vasudevan , Quoc V. Le

We propose Adam-mini, an optimizer that achieves on par or better performance than AdamW with 50% less memory footprint. Adam-mini reduces memory by cutting down the learning rate resources in Adam (i.e., $1/\sqrt{v}$). By investigating the…

Machine Learning · Computer Science 2025-02-25 Yushun Zhang , Congliang Chen , Ziniu Li , Tian Ding , Chenwei Wu , Diederik P. Kingma , Yinyu Ye , Zhi-Quan Luo , Ruoyu Sun

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of…

Selecting an optimizer is a central step in the contemporary deep learning pipeline. In this paper, we demonstrate the sensitivity of optimizer comparisons to the hyperparameter tuning protocol. Our findings suggest that the hyperparameter…

Machine Learning · Computer Science 2020-06-17 Dami Choi , Christopher J. Shallue , Zachary Nado , Jaehoon Lee , Chris J. Maddison , George E. Dahl

Neural network training can be accelerated when a learnable update rule is used in lieu of classic adaptive optimizers (e.g. Adam). However, learnable update rules can be costly and unstable to train and use. Recently, Jang et al. (2023)…

Machine Learning · Computer Science 2025-03-03 Boris Knyazev , Abhinav Moudgil , Guillaume Lajoie , Eugene Belilovsky , Simon Lacoste-Julien

A major contributor to the quality of a deep learning model is the selection of the optimizer. We propose a new dual-joint search space in the realm of neural optimizer search (NOS), along with an integrity check, to automate the process of…

Neural and Evolutionary Computing · Computer Science 2024-04-11 Brandon Morgan , Dean Hougen

The adoption of deep neural networks (DNNs) in safety-critical domains has engendered serious reliability concerns. A prominent example is hardware transient faults that are growing in frequency due to the progressive technology scaling,…

Machine Learning · Computer Science 2021-03-30 Zitao Chen , Guanpeng Li , Karthik Pattabiraman

Transformers have become the de facto backbone of modern deep learning, yet their training typically demands an advanced optimizer with adaptive learning rate like AdamW, rather than a momentum SGDW (mSGDW). Previous works show that it is…

Machine Learning · Computer Science 2025-07-24 Xianbiao Qi , Marco Chen , Wenjie Xiao , Jiaquan Ye , Yelin He , Chun-Guang Li , Zhouchen Lin

Optimization is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…

Machine Learning · Computer Science 2023-12-13 Jan Sobotka , Petr Šimánek , Daniel Vašata

Choosing the optimizer is considered to be among the most crucial design decisions in deep learning, and it is not an easy one. The growing literature now lists hundreds of optimization methods. In the absence of clear theoretical guidance…

Machine Learning · Computer Science 2021-08-12 Robin M. Schmidt , Frank Schneider , Philipp Hennig

How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows…

Machine Learning · Computer Science 2026-03-03 Tom Jacobs , Chao Zhou , Rebekka Burkholz

Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…

Machine Learning · Computer Science 2025-03-19 Dayal Singh Kalra , John Kirchenbauer , Maissam Barkeshli , Tom Goldstein

Optimization algorithms are core methods by which machine learning models iteratively minimize loss functions, update parameters, learn from data, and improve performance. Momentum SGD and AdamW represent two important optimization…

Machine Learning · Computer Science 2026-05-21 Meng Zhu , Quan Xiao , Weidong Min

Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…

Machine Learning · Computer Science 2025-10-30 Zhifeng Wang , Longlong Li , Chunyan Zeng

One of the primary reasons behind the success of neural networks has been the emergence of an array of new, highly-successful optimizers, perhaps most importantly the Adam optimizer. It is widely used for training neural networks, yet…

Machine Learning · Computer Science 2025-07-25 Benedikt Brantner

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

Machine Learning · Computer Science 2026-05-22 Saurabh Saini , Kapil Ahuja , Thomas Wick , Saurav Kumar

We propose AdaMuon, a novel optimizer that combines element-wise adaptivity with orthogonal updates for large-scale neural network training. AdaMuon incorporates two tightly coupled mechanisms: (1) an element-wise second momentum estimator…

Machine Learning · Computer Science 2025-12-25 Chongjie Si , Debing Zhang , Wei Shen

The paper presents the formulation, implementation, and evaluation of the ArcGD optimiser. The evaluation is conducted initially on a non-convex benchmark function and subsequently on a real-world ML dataset. The initial comparative study…

Machine Learning · Computer Science 2026-03-25 Nikhil Verma , Joonas Linnosmaa , Leonardo Espinosa-Leal , Napat Vajragupta

This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…

Optimization and Control · Mathematics 2024-07-08 Gang Bao , Dong Wang , Boyi Zou

Learned optimizers are increasingly effective, with performance exceeding that of hand designed optimizers such as Adam~\citep{kingma2014adam} on specific tasks \citep{metz2019understanding}. Despite the potential gains available, in…

Machine Learning · Computer Science 2021-01-20 Luke Metz , C. Daniel Freeman , Niru Maheswaranathan , Jascha Sohl-Dickstein